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Research Papers: Design and Analysis

Time-Dependent Electro–Magneto–Thermoelastic Stresses of a Poro-Piezo-Functionally Graded Material Hollow Sphere

[+] Author and Article Information
M. Jabbari

Associate Professor
Mechanical Engineering Department,
South Tehran Branch,
Islamic Azad University,
Tehran 443511365, Iran
e-mail: m_jabbari@azad.ac.ir

M. S. Tayebi

Mechanical Engineering Department,
West Tehran Branch,
Islamic Azad University,
Tehran 1949663311, Iran
e-mail: tayebi.m.s@gmail.com

1Corresponding author.

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received May 18, 2014; final manuscript received March 5, 2016; published online April 29, 2016. Assoc. Editor: Albert E. Segall.

J. Pressure Vessel Technol 138(5), 051201 (Apr 29, 2016) (12 pages) Paper No: PVT-14-1083; doi: 10.1115/1.4033089 History: Received May 18, 2014; Revised March 05, 2016

In this paper, analytical solution for time-dependent electro–magneto–thermoelastic stresses of a hollow sphere made of a fluid-saturated functionally graded porous piezoelectric material (FGPPM) is presented. All material properties, except Poisson's ratio, vary through the radial direction of the FGPPM spherical structure according to a simple power-law. The general form of thermal, mechanical, and electric potential boundary conditions is considered on the internal and external surfaces of the sphere, and the sphere is under constant electrical and magnetic fields. Stress–strain and strain–displacement relations are used to obtain stress–displacement equations, and then by putting stress–displacement equations in the equilibrium equation, Navier equation is acquired. The homogenous differential heat conduction equation is solved. The nonhomogenous differential Navier equation is solved for two cases. At first, creep strains are ignored and the initial electro–magneto–thermoelastic stresses are obtained. Then considering creep strains singly, the creep stress rates are obtained. Finally, time-dependent creep stress distributions at any time ti are attained.

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References

Qin, Q.-H. , 2001, Fracture Mechanics of Piezoelectric Materials, WIT, Southampton, UK.
Takeuti, Y. , and Tanigawa, Y. , 1982, “ Transient Thermal Stresses of a Hollow Sphere Due to Rotating Heat Source,” J. Therm. Stresses, 5(3–4), pp. 283–298. [CrossRef]
Obata, Y. , and Noda, N. , 1994, “ Steady Thermal Stress in a Hollow Circular Cylinder and a Hollow Sphere of Functionally Gradient Materials,” J. Therm. Stresses, 17(3), pp. 471–487. [CrossRef]
Zimmerman, R. W. , and Lutz, M. P. , 1996, “ Thermal Stresses and Effective Thermal Expansion Coefficient of Functionally Graded Sphere,” J. Therm. Stresses, 19(1), pp. 39–54. [CrossRef]
Jabbari, M. , Sohrabpourb, S. , and Eslami, M. R. , 2002. “ Mechanical and Thermal Stresses in A Functionally Graded Hollow Cylinder Due to Radially Symmetric Loads,” Int. J. Pressure Vessels Piping, 79(7), pp. 493–497. [CrossRef]
Eslami, M. R. , Babaei, M. H. , and Poultangari, R. , 2005, “ Thermal and Mechanical Stresses in a Functionally Graded Thick Sphere,” Int. J. Pressure Vessels Piping, 82(7), pp. 522–527. [CrossRef]
Ding, H. J. , and Chen, W. Q. , 2001, Three Dimensional Problems of Piezoelasticity, Nova Science, New York.
Sinha, D. K. , 1962, “ Note on the Radial Deformation of a Piezoelectric, Polarized Spherical Shell With a Symmetrical Distribution,” J. Acoust. Soc. Am., 34(8), pp. 1073–1075. [CrossRef]
Shul'ga, N. A. , 1990, “ Radial Electroelastic Vibrations of a Hollow Piezoceramic Sphere,” Soviet Appl. Mech., 26(8), pp. 731–734. [CrossRef]
Chen, W. Q. , and Shioya, T. , 2001, “ Piezothermoelastic Behavior of a Pyroelectric Spherical Shell,” J. Therm. Stresses, 24(2), pp. 105–120. [CrossRef]
Wu, C. C. M. , Kahn, M. , and Moy, W. , 1996, “ Piezoelectric Ceramics With Functionally Gradients: A New Application in Material Design,” J. Am. Ceram. Soc., 79(3), pp. 809–812. [CrossRef]
Shelley, W. F. , Wan, S. , and Bowman, K. J. , 1999, “ Functionally Graded Piezoelectric Ceramics,” Mater. Sci. Forum, 308–311, pp. 515–520. [CrossRef]
Zhu, X. H. , Zu, J. , Meng, Z. Y. , Zhu, J. M. , Zhou, S. H. , Li, Q. , Liu, Z. , and Ming, N. , 2000, “ Micro Displacement Characteristics and Microstructures of Functionally Graded Piezoelectric Ceramic Actuator,” Mater. Des., 21(6), pp. 561–566. [CrossRef]
Chen, W. Q. , Lu, Y. , Ye, G. R. , and Cai, J. B. , 2002, “ 3D Electroelastic Fields in a Functionally Graded Piezoceramic Hollow Sphere Under Mechanical and Electric Loadings,” Arch. Appl. Mech., 72(1), pp. 39–51. [CrossRef]
Dai, H. L. , and Wang, X. , 2005, “ Stress Wave Propagation in Laminated Piezoelectric Spherical Shells Under Thermal Shock and Electric Excitation,” Eur. J. Mech. A/Solids, 24(2), pp. 263–276. [CrossRef]
Dai, H. L. , and Wang, X. , 2005, “ Thermo-Electro-Elastic Transient Responses in Piezoelectric Hollow Structures,” Int. J. Solids Struct., 42(3–4), pp. 1151–1171. [CrossRef]
Ootao, Y. , and Tanigawa, Y. , 2007, “ Transient Piezothermoelastic Analysis for a Functionally Graded Thermopiezoelectric Hollow Sphere,” Compos. Struct., 81(4), pp. 540–549. [CrossRef]
Ben Salah, I. , Njeh, A. , and Ben Ghozlen, M. H. , 2012, “ A Theoretical Study of the Propagation of Rayleigh Waves in a Functionally Graded Piezoelectric Material (FGPM),” Mater. Sci. Eng., 52(2), pp. 306–314.
Bowen, C. R. , Perry, A. , Lewis, A. C. F. , and Kara, H. , 2004, “ Processing and Properties of Porous Piezoelectric Materials With High Hydrostatic Figures of Merit,” J. Eur. Ceram. Soc., 24(2), pp. 541–545. [CrossRef]
Chen, W. Q. , Ding, H. J. , and Xu, R. Q. , 2001, “ Three-Dimensional Free Vibration Analysis of a Fluid-Filled Piezoceramic Hollow Sphere,” Comput. Struct., 79(6), pp. 653–663. [CrossRef]
Jabbari, M. , Karampour, S. , and Eslami, M. R. , 2011, “ Radially Symmetric Steady State Thermal and Mechanical Stresses of a Poro FGM Hollow Sphere,” ISRN Mech. Eng., 2011, p. 305402.
Jabbari, M. , Karampour, S. , and Eslami, M. R. , 2013, “ Steady State Thermal and Mechanical Stresses of a Poro-Piezo-FGM Hollow Sphere,” Meccanica, 48(3), pp. 699–719. [CrossRef]
Finnie, I. , and Heller, W. R. , 1959, Creep of Engineering Materials, McGraw-Hill, New York.
Yang, Y. Y. , 2000, “ Time-Dependent Stress Analysis in Functionally Graded Material,” Int. J. Solids Struct., 37(51), pp. 7593–7608. [CrossRef]
Rangaraj, S. , and Kokini, K. , 2002, “ Time-Dependent Behavior of Ceramic-Metal Particulate Composites,” Mech. Time-Dependent Mater., 6(2), pp. 171–191. [CrossRef]
Chen, J. J. , Tu, S. H. , Xuan, Z. H. , and Wang, Z. H. , 2006, “ Creep Analysis for a Functionally Graded Cylinder Subjected to Internal and External Pressure,” J. Strain Anal., 42(2), pp. 69–77. [CrossRef]
Dai, H. L. , and Fu, Y. M. , 2007, “ Magnetothermoelastic Interactions in Hollow Structures of Functionally Graded Material Subjected to Mechanical Load,” Int. J. Pressure Vessels Piping, 84(3), pp. 132–138. [CrossRef]
Arani, A. G. , Salari, M. , Khademizadeh, H. , and Arefmanesh, A. , 2009, “ Magnetothermoelastic Transient Response of a Functionally Graded Thick Hollow Sphere Subjected to Magnetic and Thermoelastic Fields,” Arch. Appl. Mech., 79, pp. 481–497. [CrossRef]
Loghman, A. , Ghorbanpour Arani, A. , Amir, S. , and Vajedi, A. , 2010, “ Magnetothermoelastic Creep Analysis of Functionally Graded Cylinders,” Int. J. Pressure Vessels Piping, 87(7), pp. 389–395. [CrossRef]
Loghman, A. , Ghorbanpour, A. A. , and Aleayoub, S. M. A. , 2011, “ Time-Dependent Creep Stress Redistribution Analysis of Functionally Graded Spheres,” Mech. Time-Dependent Mater., 15(4), pp. 353–365. [CrossRef]
Loghman, A. , Aleayoub, S. M. A. , and Sadi, M. H. , 2012, “ Time-Dependent Magnetothermoelastic Creep Modeling of FGM Spheres Using Method of Successive Elastic Solution,” Appl. Math. Model., 36(2), pp. 836–845. [CrossRef]
Dai, H. L. , Jiang, H. J. , and Yang, L. , 2012, “ Time-Dependent Behaviors of a FGPM Hollow Sphere Under the Coupling of Multi-Fields,” Solid State Sci., 14(5), pp. 587–597. [CrossRef]
Dai, H. L. , Fu, Y. M. , and Yang, J. H. , 2007, “ Electromagnetoelastic Behaviors of Functionally Graded Piezoelectric Solid Cylinder and Sphere,” Acta Mech. Sin., 23(1), pp. 55–63. [CrossRef]
Hetnarski, R. B. , and Eslami, M. R. , 1999, Thermal Stresses—Advanced Theory and Applications, Springer, New York.
Mendelson, A. , 1968, Plasticity Theory and Applications, Macmillan, New York.

Figures

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Fig. 1

Temperature distribution in the FGPPM hollow sphere with various β

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Fig. 2

Radial displacement distribution in the FGPPM hollow sphere with various β at zero time

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Fig. 3

Electric potential distribution in the FGPPM hollow sphere with various β at zero time

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Fig. 4

Radial stress distribution in the FGPPM hollow sphere with various β at zero time

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Fig. 5

Hoop stress distribution in the FGPPM hollow sphere with various β at zero time

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Fig. 6

Effective stress distribution in the FGPPM hollow sphere with various β at zero time

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Fig. 7

Radial stress rate distribution of the FGPPM hollow sphere with various β at zero time

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Fig. 8

Hoop stress rate distribution of the FGPPM hollow sphere with various β at zero time

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Fig. 9

Radial creep stress redistribution of the FGPPM hollow sphere where β = −1.5

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Fig. 10

Hoop creep stress redistribution of the FGPPM hollow sphere where β = −1.5

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Fig. 11

Effective creep stress redistribution of the FGPPM hollow sphere where β = −1.5

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Fig. 12

Radial creep stress redistribution of the FGPPM hollow sphere where β = 1

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Fig. 13

Hoop creep stress redistribution of the FGPPM hollow sphere where β = 1

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Fig. 14

Effective creep stress redistribution of the FGPP hollow sphere where β = 1

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Fig. 15

Radial displacement distribution of the FGPPM hollow sphere with various φb for the case β = 1 at zero time

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Fig. 16

Radial stress distribution of the FGPPM hollow sphere with various φb for the case β = 1 at zero time

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Fig. 17

Hoop stress distribution of the FGPPM hollow sphere with various φb for the case β = 1 at zero time

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Fig. 18

Effective stress distribution of the FGPPM hollow sphere with various φb for the case β = 1 at zero time

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Fig. 19

Radial stress rate distribution of the FGPPM hollow sphere with various φb for the case β = 1 at zero time

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Fig. 20

Hoop stress rate distribution of the FGPPM hollow sphere with various φb for the case β = 1 at zero time

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